Simplify the following expression: $ k = \dfrac{-10n + 5}{-8} - \dfrac{-10}{9} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{-10n + 5}{-8} \times \dfrac{9}{9} = \dfrac{-90n + 45}{-72} $ Multiply the second expression by $\dfrac{-8}{-8}$ $ \dfrac{-10}{9} \times \dfrac{-8}{-8} = \dfrac{80}{-72} $ Therefore $ k = \dfrac{-90n + 45}{-72} - \dfrac{80}{-72} $ Now the expressions have the same denominator we can simply subtract the numerators: $k = \dfrac{-90n + 45 - 80 }{-72} $ Distribute the negative sign: $k = \dfrac{-90n + 45 - 80}{-72}$ $k = \dfrac{-90n - 35}{-72}$ Simplify the expression by dividing the numerator and denominator by -1: $k = \dfrac{90n + 35}{72}$